Web Search for Mehler integrals
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Phil's working notes dated 1.28.11 recording a web search for integrals involving Mehler or conical functions. They go through about seven references, including Google Books previews, an encyclopedia entry, a JSTOR paper and lectures by Sneddon on the Mehler-Fock transform, and mention a certain Felson. He judges most of them too technical or not useful for finding a table of integrals or methods for evaluating them. The screenshots are missing from the extracted text.
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Web Search for Mehler integrals PhL 1.28.11
Searching on "integrals involving conical", I basically get one reference to a certain Felson, but it is in J. Math and Phys which only BYU has (discontinued journal).
Nothing in "integrals involving Mehler". But that led to this book:
Reference 1
which certainly seems on topic, and a whole book! Here are some clips, where our friend Felson appears right away:
At this point we hit a missing page, but he is doing μ plane stuff, not so important to me. There is nothing else in this Google book view for this book. Here is the contents
and perhaps Chapter 4 might have what I want. This book is not at Marriott.
Reference 2
Certainly another on topic book!
The book then goes on to prove technical Mehler related theorems and that fills out this chapter
Really this is not what I am looking for right now, convergence theorems and such.
Reference 3
The contents are concealed, rather amazing. They do reel off some integral representations
and then versions of the same with μ present. Then some interesting claims
And here is a little discussion I was about to write, but they have done it for me
But nothing else useful to me in this preview. $73 for the PDF!
Reference 4.
Here is a paper I can probably get from Jstor
but it is not likely to have what I need.
Reference 5. This is from Encyclopedia of Mathematics by Hazewinkel
There is good old Sneddon again! That book might have something for me and is just sitting there
Reference 6 These are the guys who did the above encyclopedia entry:
The section then gets very technical, reviewing lots of people's results. Nothing on how to do integrals!
Reference 7 Lectures by Sneddon specifically on M-F
I don't know how to narrow down to finding a table of integrals or instructions how to do them! My web search has not really produced anything useful.